Inspired by empirical studies of networked systems such as the Internet, social networks, and biological networks, researchers have in recent years developed a variety of techniques and models to help us understand or predict the behavior of these systems. Here we review developments in this field, including such concepts as the small-world effect, degree distributions, clustering, network correlations, random graph models, models of network growth and preferential attachment, and dynamical processes taking place on networks.

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The Structure and Function of Complex Networks

Recent developments in the quantitative analysis of complex networks, based largely on graph theory, have been rapidly translated to studies of brain network organization. The brain's structural and functional systems have features of complex networks--such as small-world topology, highly connected hubs and modularity--both at the whole-brain scale of human neuroimaging and at a cellular scale in non-human animals. In this article, we review studies investigating complex brain networks in diverse experimental modalities (including structural and functional MRI, diffusion tensor imaging, magnetoencephalography and electroencephalography in humans) and provide an accessible introduction to the basic principles of graph theory. We also highlight some of the technical challenges and key questions to be addressed by future developments in this rapidly moving field.

Complex brain networks: graph theoretical analysis of structural and functional systems

A complementary DNA for the Aequorea victoria green fluorescent protein (GFP) produces a fluorescent product when expressed in prokaryotic (Escherichia coli) or eukaryotic (Caenorhabditis elegans) cells. Because exogenous substrates and cofactors are not required for this fluorescence, GFP expression can be used to monitor gene expression and protein localization in living organisms.

http://science.sciencemag.org/content/sci/263/5148/802.full.pdf

Green fluorescent protein as a marker for gene expression

Complex networks are studied across many fields of science. To uncover their structural design principles, we defined “network motifs,” patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks. We found such motifs in networks from biochemistry, neurobiology, ecology, and engineering. The motifs shared by ecological food webs were distinct from the motifs shared by the genetic networks of Escherichia coli and Saccharomyces cerevisiae or from those found in the World Wide Web. Similar motifs were found in networks that perform information processing, even though they describe elements as different as biomolecules within a cell and synaptic connections between neurons in Caenorhabditis elegans. Motifs may thus define universal classes of networks. This

/pdf/network-motifs-simple-building-blocks-of-complex-networks-4arf58zy7p.pdf

Network Motifs: Simple Building Blocks of Complex Networks

The structure and connectivity of the nervous system of the nematode Caenorhabditis elegans has been deduced from reconstructions of electron micrographs of serial sections. The hermaphrodite nervous system has a total complement of 302 neurons, which are arranged in an essentially invariant structure. Neurons with similar morphologies and connectivities have been grouped together into classes; there are 118 such classes. Neurons have simple morphologies with few, if any, branches. Processes from neurons run in defined positions within bundles of parallel processes, synaptic connections being made en passant. Process bundles are arranged longitudinally and circumferentially and are often adjacent to ridges of hypodermis. Neurons are generally highly locally connected, making synaptic connections with many of their neighbours. Muscle cells have arms that run out to process bundles containing motoneuron axons. Here they receive their synaptic input in defined regions along the surface of the bundles, where motoneuron axons reside. Most of the morphologically identifiable synaptic connections in a typical animal are described. These consist of about 5000 chemical synapses, 2000 neuromuscular junctions and 600 gap junctions.

The structure of the nervous system of the nematode Caenorhabditis elegans

The neural pathways for touch-induced movement in Caenorhabditis elegans contain six touch receptors, five pairs of interneurons, and 69 motor neurons. The synaptic relationships among these cells have been deduced from reconstructions from serial section electron micrographs, and the roles of the cells were assessed by examining the behavior of animals after selective killing of precursors of the cells by laser microsurgery. This analysis revealed that there are two pathways for touch-mediated movement for anterior touch (through the AVD and AVB interneurons) and a single pathway for posterior touch (via the PVC interneurons). The anterior touch circuitry changes in two ways as the animal matures. First, there is the formation of a neural network of touch cells as the three anterior touch cells become coupled by gap junctions. Second, there is the addition of the AVB pathway to the pre- existing AVD pathway. The touch cells also synapse onto many cells that are probably not involved in the generation of movement. Such synapses suggest that stimulation of these receptors may modify a number of behaviors.

https://www.jneurosci.org/content/jneuro/5/4/956.full.pdf

The neural circuit for touch sensitivity in Caenorhabditis elegans

The nervous system of Caenorhabditis elegans is arranged as a series of fibre bundles which run along internal hypodermal ridges. Most of the sensory integration takes place in a ring of nerve fibres which is wrapped round the pharynx in the head. The body muscles in the head are innervated by motor neurones in this nerve ring while those in the lower part of the body are innervated by a set of motor neurones in a longitudinal fibre bundle which joins the nerve ring, the ventral cord. These motor neurones can be put into five classes on the basis of their morphology and synaptic input. At any one point along the cord only one member from each class has neuromuscular junctions. Members of a given class are arranged in a regular linear sequence in the cord and have non-overlapping fields of motor synaptic activity, the transition between fields of adjacent neurones being sharp and well defined. Members of a given class form gap junctions with neighbouring members of the same class but never to motor neurones of another class. Three of the motor neurone classes receive their synaptic input from a set of interneurones coming from the nerve ring. These interneurones can in turn be grouped into four classes and each of the three motor neurone classes receives its synaptic input from a unique combination of interneurone classes. The possible developmental and functional significance of these observations is discussed.

The structure of the ventral nerve cord of Caenorhabditis elegans

IDENTIFICATION of the genes orchestrating neurogenesis would greatly enhance our understanding of this process. Genes have been identified that specify neuron type (for examplecut1 and numb2 inDrosophila andmec-3 in Caenorhabditis elegans3) and process guidance (for example,unc-5,unc-6 andunc-40 inC. elegans4and thefas-1 gene of Drosophila5). We sought genes defining synaptic specificity by identifying mutations that alter synaptic connectivity in the motor circuitry in the nematodeC.elegans. We used electron microscopy of serial sections6 to recon-struct the ventral nerve-cords of uncoordinated (unc) mutants7,8 that have distinctive locomotory choreographies. Here we describe the phenotype of mutations in theunc-4 gene in which a locomotory defect is correlated with specific changes in synaptic input to a subset of the excitatory VA motor neurons, normally used in reverse locomotion. The circuitry alterations do not arise because of the inaccessibility of the appropriate synaptic partners, but are a consequence of changes in synaptic specificity. The VA motor neurons with altered synaptic inputs are all lineal sisters of VB motor neurons; the VA motor neurons without VB sisters have essentially the same synaptic inputs as in wild-type animals. The normal function of the wild-type allele of unc-4 may thus be to invoke the appropriate synaptic specificities to VA motor neurons produced in particular developmental contexts.

Mutations in the Caenorhabditis elegans unc-4 gene alter the synaptic input to ventral cord motor neurons.

During the course of normal embryonic and post-embryonic development, 131 cells in a Caenorhabditis elegans hermaphrodite undergo programmed cell death. Loss of function mutations in either of the genes ced-3 or ced-4 abolish cell deaths, enabling these ‘undead’ cells to survive and be incorporated into the adult with no obvious deleterious consequences. Ultrastructural reconstructions have shown that undead cells exhibit many differentiated characteristics. Most of the reconstructed cells appeared to be neurons with all the characteristic features associated with such cells, such as processes, synaptic vesicles and presynaptic specializations. However, clear morphological differences were seen among the undead neurons, suggesting a diversity of cell type. One of the reconstructed cells was a rectal epithelial cell, which had displaced its lineal sister that normally functions in this role. Removal of the ability to undergo programmed cell death by mutation therefore reveals a diversity of cryptic differentiated states that are acquired by cells that normally are destined to die.

Eileen Southgate

Papers

The structure of the nervous system of the nematode Caenorhabditis elegans

The neural circuit for touch sensitivity in Caenorhabditis elegans

The structure of the ventral nerve cord of Caenorhabditis elegans

Mutations in the Caenorhabditis elegans unc-4 gene alter the synaptic input to ventral cord motor neurons.

On the nature of undead cells in the nematode Caenorhabditis elegans